Find each measurement indicated. Round your answers to the nearest tenth. Fi

pamangking8 2021-11-18 Answered
Find each measurement indicated. Round your answers to the nearest tenth.
Find BC
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Expert Answer

Kara Dillon
Answered 2021-11-19 Author has 78 answers

Step 1
image

Since, we are given the length of the sides AC and AB withmeasurement of 10 cm and 13 cm of a non right angled triangles with \(\displaystyle{137}^{{\circ}}\) between them
Our aim is to find the length of the side BC of a triangle i.e, to find the value of \(\displaystyle{x}=?\)
Step 2
image Using Cosine Rule in finding the unlown lenth of the side which states that:
For any non−right angled triangle with sides a, b and c:−
\(\displaystyle{b}^{{{2}}}={c}^{{{2}}}+{a}^{{{2}}}-{2}{c}{a}{\cos{{B}}}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}={\left({10}\right)}^{{{2}}}+{\left({13}\right)}^{{{2}}}-{2}\times{10}\times{13}\times{\cos{{\left({137}^{{\circ}}\right)}}}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}={100}+{169}-{\left({260}\times{0.334}\right)}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}={269}-{86.88}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}={182.12}\)
\(\displaystyle\Rightarrow{x}=\sqrt{{{182.12}}}\)
\(\displaystyle\Rightarrow{x}={13.49}{c}{m}\)
On rounding off to the nearest tenth we have \(\displaystyle{x}={13.5}{c}{m}\)
Therefore, the length of the side BC is 13.5 cm.

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